
where \(C=C(p,q)>0\)  is a constant. Moreover, from the proof of [1]}, we have
\(\int _{B_i}\int _{B_i} \frac{|\psi _i(x)-\psi _i(y)|^\ell }{|x-y|^{N+s\ell }}(\tilde{w}_i(x)^\ell + \tilde{w}_i(y)^\ell )dxdy&\le c \frac{2^{ip}}{\ell (1-s)}\frac{1}{\tilde{k}^{p-\ell }}\frac{r^N}{r^{s\ell }} \mathchoice{{\displaystyle {\textstyle -}{\int } }\hbox{$\textstyle -$ }}{\hspace{0.0pt}}{-}{.}6\) 
